The dynamic behaviour of multi-span continuous bridges under a moving vehicular load is investigated by considering the effect of interaction between the vehicle and the bridge pavement, the torsion in the bridge due to eccentrically placed vehicles and the randomness of the surface irregularity of the pavement. The response of the bridge is obtained in the time domain by using an iterative procedure employed at each time step to take into account the non-linearity of the pavement-vehicle interactive force. The solution procedure is made efficient by utilizing a continuum approach for determining the eigenfunctions of the bridge deck, and by obtaining the deck response at each iteration with the help of a few closed form (recursive) expressions. The method of analysis is used to perform a parametric study to show the influence of some important parameters on the response of the bridge.